Finite Group Databasebeta

← #15674694

Subgroups — #15674694

Order 2944.

262 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 67 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10625122C211yesmaximal, characteristic
2C2×#10625004C211yesmaximal, characteristic, complemented
3C2×#10624992C211yesmaximal, characteristic, complemented
4C2×#10625006C211yesmaximal, characteristic, complemented
5#13092384C211yesmaximal, characteristic
6#13092186C211yesmaximal, characteristic, complemented
7C23×#417C211yesmaximal, characteristic
8C2×#41×C23C2211yescharacteristic
9C22×Dic46C2211yescharacteristic
10C2×M16×C23C2211yescharacteristic
11C2×C4⋊C4×C23C2211yescharacteristic
12#10625122—22no—
13#10625122—22no—
14C2×#67275—21no—
15C2×#67273—21no—
16C2×#67267C2211yescharacteristic
17C2×#67267C2211yescharacteristic
18C22×C23⋊C8C2211yescharacteristic
19C23×#103—21no—
20C23×#102—21no—
21C22⋊(C23⋊C8)—22no—
22#10625006—22no—
23#10625004—22no—
24#10624992—22no—
25#41×C23—21no—
26#41×C23—21no—
27#41×C23—21no—
28#41×C23—21no—
29C2×Q8×C23D411yescharacteristic
30C2×D4×C23—21no—
31C2×D4×C23D411yescharacteristic
32C22×C4×C23—21no—
33C22×C4×C23—21no—
34C22×C4×C23C2311yescharacteristic
35C22×Dic23—21no—
36C2×Dic46—21no—
37C2×Dic46—21no—
38C2×Dic46—21no—
39C2×Dic46—21no—
40C2×Dic46—21no—
41C2×Dic46D412yes—
42M16×C23—21no—
43M16×C23—21no—
44C2×C8×C23—21no—
45C4⋊C4×C23—21no—
46C4⋊C4×C23—21no—
47#67275—24no—
48#67273—24no—
49#67267—21no—
50#67267—21no—
51#67267—21no—
52#67267D412yes—
53C2×C23⋊C8—21no—
54C2×C23⋊C8—21no—
55C2×C23⋊C8—21no—
56C2×C23⋊C8—21no—
57C2×C23⋊C8D412yes—
58C23×C23—21no—
59C23×C23#4111yescharacteristic
60Q8×C23—21no—
61Q8×C23—21no—
62D4×C23—21no—
63D4×C23—21no—
64D4×C23—41no—
65D4×C23—41no—
66C2×C4×C23—21no—
67C2×C4×C23—41no—
68C2×C4×C23—41no—
69C2×C4×C23—41no—
70C2×C4×C23—81no—
71C2×C4×C23C2×D411yescharacteristic
72C2×C4×C23C2×D411yescharacteristic
73C2×C4×C23C2×D411yescharacteristic
74C2×C4×C23C2×D411yescharacteristic
75C2×C4×C23#4111yescharacteristic
76C2×C4×C23#4111yescharacteristic
77C2×Dic23—22no—
78C2×Dic23—41no—
79C2×Dic23—41no—
80Dic46—22no—
81Dic46—22no—
82Dic46—41no—
83Dic46—41no—
84C8×C23—41no—
85C23⋊C8—22no—
86C23⋊C8—22no—
87C23⋊C8—41no—
88#2052—231nomaximal, Sylow
89C22×C23—21no—
90C22×C23—21no—
91C22×C23—41no—
92C22×C23—41no—
93C22×C23—41no—
94C22×C23#12111yescharacteristic
95C22×C23#12311yescharacteristic
96C22×C23#12411yescharacteristic
97C4×C23—41no—
98C4×C23—81no—
99C4×C23#12011yescharacteristic
100C4×C23#12111yescharacteristic
101C4×C23#12111yescharacteristic
102C4×C23#12311yescharacteristic
103Dic23—42no—
104C2×#137—231no—
105C2×#108—231no—
106#417D2311yescharacteristic
107C2×#103—231no—
108C2×#101—231no—
109#408—231no—
110#343—231no—
111C2×C23—21no—
112C2×C23—21no—
113C2×C23—81no—
114C2×C23#39411yescharacteristic
115C2×C23#47111yescharacteristic
116C2×C23#47311yescharacteristic
117C2×#41C2×D2311yescharacteristic
118C22×Q8—231no—
119#137—462no—
120#137—462no—
121C2×Q16—461no—
122C2×SD16—461no—
123C2×M16—231no—
124C2×M16—231no—
125C2×M16C2×D2311yescharacteristic
126C22×C8—231no—
127C2×C4⋊C4C2×D2311yescharacteristic
128#108—462no—
129#103—21no—
130#103—462no—
131#102—21no—
132#101—462no—
133C22⋊C8—462no—
134C23#205211yescharacteristic, complemented, Sylow
135#41—21no—
136#41—21no—
137#41—21no—
138#41—21no—
139C2×Q8—232no—
140C2×Q8—461no—
141C2×Q8—461no—
142C2×Q8—461no—
143C2×Q8—461no—
144C2×Q8—461no—
145C2×Q8C22⋊D2311yescharacteristic
146C2×D4—21no—
147C2×D4C22⋊D2311yescharacteristic
148C22×C4—21no—
149C22×C4—21no—
150C22×C4—461no—
151C22×C4C22×D2311yescharacteristic
152Q16—464no—
153SD16—464no—
154M16—21no—
155M16—21no—
156M16—232no—
157M16—461no—
158M16—461no—
159M16—461no—
160C2×C8—21no—
161C2×C8—232no—
162C2×C8—461no—
163C2×C8—461no—
164C2×C8—461no—
165C2×C8—461no—
166C4⋊C4—21no—
167C4⋊C4—21no—
168C23—21no—
169C23#6729011yescharacteristic
170Q8—21no—
171Q8—21no—
172Q8—462no—
173Q8—462no—
174Q8—921no—
175Q8—921no—
176D4—21no—
177D4—21no—
178D4—41no—
179D4—41no—
180C2×C4—21no—
181C2×C4—41no—
182C2×C4—41no—
183C2×C4—41no—
184C2×C4—81no—
185C2×C4—462no—
186C2×C4—921no—
187C2×C4—921no—
188C2×C4#6728811yescharacteristic
189C2×C4#6728811yescharacteristic
190C2×C4D4×D2311yescharacteristic
191C2×C4D4×D2311yescharacteristic
192C2×C4D4×D2311yescharacteristic
193C2×C4C2×C22⋊D2311yescharacteristic
194C8—41no—
195C8—462no—
196C8—462no—
197C8—921no—
198C22—21no—
199C22—21no—
200C22—41no—
201C22—41no—
202C22—41no—
203C22#1062505411yescharacteristic
204C22#1062505611yescharacteristic
205C22#1062511011yescharacteristic
206C4—41no—
207C4—81no—
208C4—922no—
209C4#1062505511yescharacteristic
210C4#1062505511yescharacteristic
211C4#1062510011yescharacteristic
212C4#1062510811yescharacteristic
213C2—21no—
214C2—21no—
215C2—81no—
216C2#1309233211yescharacteristic
217C2#1309267811yescharacteristic
218C2#1309269011yescharacteristic
subgroupG/H
centerC22#10625110
commutator, cosocleC22×C4×C23C23
FrattiniC22×C4C22×D23
FittingC23×#417C2
socleC22×C23#121
prime radicalC2×#41×C23C22
hypercenter#417D23
hypocenterC23#2052
LCSG ▷ C22×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#10625004C2semidirect
3. C2×#10624992C2semidirect
4. C2×#10625006C2semidirect
6. #13092186C2semidirect
134. C23#2052semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#106251222
C2×#106250042
C2×#106249922
C2×#106250062
#130923842
#130921862
C23×#4172
#205223